三阶色散对超高斯型脉冲传输特性的影响

Influence of the third-order dispersion on propagation properties of super-Gaussian pulses in optical fibers

从修正的非线性Schr(o|¨)dinger方程出发,采用变分法,导出了在三阶色散情况下超高斯型脉冲参数随传输距离的演化方程组及其解,讨论了三阶色散对光纤中不同锐度超高斯脉冲传输特性的影响.求出了振幅与脉宽、脉宽与啁啾、啁啾与频率及中心位置之间的三个解析约束关系,得出了脉宽随传输距离演化的解析解,用龙格-库塔法进行数值求解描绘了不同锐度下三阶色散对光纤中超高斯脉冲脉宽的影响.结果表明:振幅和脉宽满足绝热特性,色散系数增大到0.3或脉冲前后沿锐度系数m≥3时,脉冲信号便会明显地展宽,其周期也大幅度地变大。

The modified nonlinear SchrSdinger equation and variational method are used to derive the evolution equations for the parameters of super-Gaussian pulse and their analytic solutions. The influence of the third-order dispersion on the propagation properties in different sharpness super-Gaussian pulses in optical fibers is discussed. Three restraint relations between amplitude and pulse width, pulse width and chirp, chirp and frequency and the center are derived. Analytical solution about the evolution of pulse-width versus propagation distance is obtained. By using Runge-Kutta algorithm, influence of the third-order dispersion and the degree of the pulse＇s edge sharpness on the pulse-width is described. The results indicate that the amplitude and pulse width satisfy the adiabatic relation, when the dispersion coefficient increases to around 0.3 or the pulse sharpness coefficient m 〉 3, the pulse signal will obviously be stretched, its cycle will significantly be larger.